Some minimization theorems in generating spaces of quasi-metric family and applications

摘要

In this paper, we establish new nonconvex minimizatiion theorems in generating spaces of quasi-metric family. As consequences, we obtain a generalized form of Downing-Kirk's fixed point theorem in the same spaces. Some applications of these results to fuzzy metric spaces in the sense of Kaleva and Seikkala and probabilistic metric spaces are presented.